A recent development in the theory of M-sets has paved a new means of an approach to CH. Here we further clarify the theory and form part two of our previous paper[P]. The set B i will be used to represent binary numbers. A set of positions associated with a one symbol we will denote by pos Elements of pos we will denote by p(1) j. Sets of transformations T i. A knowable set H is denoted by K(H...

Most real world engineering design problems, such as cross-country water mains, include combinations of continuous, discrete, and binary value decision variables. Very often, the binary decision variables associate with the presence and/or absence of some nominated alternatives or project’s components. This study extends an existing continuous Ant Colony Optimization (ACO) algorithm to simultan...

The decomposition of the overall effect a treatment into direct and indirect effects is here investigated with reference to recursive system binary random variables. We show how, for single mediator context, marginal measured on log odds scale can be written as sum plus residual term that vanishes under some specific conditions. then extend our definitions situations involving multiple mediator...

In response to the transition by the United States Nuclear Regulatory Commission (NRC) to a risk-informed, performance-based fire protection rulemaking standard, Fire Probabilistic Risk Assessment (PRA) methods have been improved, particularly in the areas of advanced fire modeling and computational methods. As the methods for the quantification of fire risk are improved, the methods for the qu...

A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X + Y is symmetric about 0. In cases where the distribution of X is symmetric about its mean, it is easy to see that the constant random variable Y = −EX is a minimum-variance independent symmetrizer. Taking Y to have the same distribution as −X clearly...